The bounds of a volume to be searched by a radar system seeking to acquire a target can be limited if a cue is available as to the likely location of the target within a larger searchable volume at the time of the search. A volume likely to contain the target, termed a covariance volume, can be determined from the cue. The cue can derive from the coordinates of the target in space at a previous time when the target was acquired, possibly further taking into account an observed velocity vector and other knowledge of the target. The probability of the target being at one location or another within the volume could be variable, but for simplicity, it may be assumed that the covariance volume is simply a volume defined by shape and size, in which the target is likely to reside with a predetermined threshold of probability. It is desirable to locate the target dependably and quickly, and/or to update the target location frequently. Therefore, it is desirable accurately to limit the search to an acquisition volume that encompasses all locations within the covariance volume and wastes no time on locations that are outside of the covariance volume.
The cue may be provided in part from signals from a remote radar that acquired the target at one or more earlier times. There are several measures of uncertainty such as the correspondence of the location coordinate systems of the local and remote radars, the tolerance in the remote radar's measurements, displacement due to changes in direction or speed, etc. Given these uncertainties and optionally also accounting for assumptions about the nature of the target, an estimated present position can be inferred, surrounded by a span of spatial uncertainty, thereby defining a covariance volume in space according to the coordinate system employed by the local radar system that is searching for the target. In one arrangement, the covariance volume can be defined by the location, dimensions and orientation of an ellipsoid. This is the volume to be searched, where the target is expected to be found. The search volume, namely the acquisition volume, is limited to or at least concentrated on the covariance volume.
The radar emits at least one pencil beam and at successive time periods aims the beam at angularly displaced positions. The lines of the angularly displaced beams diverge or radiate from the radar system; and the beam width widens proceeding away from the radar system. Preferably in a repeating cycle, the radar aims at each beam position for a sufficient dwell time to account for a time delay in which a signal emitted from the radar can impinge on a target at a maximum range, be reflected, and for the echo to be received at the radar. A given echo return time corresponds to a given range from the radar. From the succession of beam emissions and possible returning echoes after a predetermined time, one can define an acquisition face, although the beams are multiplexed in time divisions.
The beams have a beam width that is sufficiently large, and the beams are aimed at angles incrementally displaced by a small enough angle, so that the beams overlap and effectively encompass all the area of the acquisition face. The area of the acquisition face increases with increasing range from the radar due to the angular divergence of the beams and the radiation of the beam directions from an origin at the radar system. At any given range (namely a given distance from the radar), the arrayed beams have horizontal limits (namely a span of azimuth or laterally diverging angles) and vertical limits (a span of elevation or vertically diverging angles). The radar system is capable of searching the entire volume between the limits of azimuth and elevation and between minimum and maximum ranges that are determined from the geometry of the system and considerations of timing and minimum echo signal strength. But the control system of the radar advantageously limits the azimuth and elevation of the beam directions used, and optionally can adjust to less than full dwell time, so as to search specifically a predetermined covariance volume that is smaller than the maximum volume of which the system is capable of searching, when seeking or tracking a target.
The distances between a selected maximum and minimum range and the angles between selected limits of azimuth and elevation define an acquisition volume. If the ranges and angular spans are equal, the search volume is shaped as a truncated spherical section. However the covariance volume typically is not a truncated spherical section, and instead may be, for example, a covariance ellipsoid volume that is located, dimensioned and oriented based on the target location cue. What is needed are ways to adjust the extents of the search volume, between angular limits of azimuth and elevation, and between minimum and maximum limits of range, to confine the search as near as possible to the covariance volume, e.g., a covariance ellipsoid.
For cued target acquisition by a local radar system, the volume of uncertainty (e.g., the covariance ellipsoid) may be derived from results of an earlier acquisition of the target. The earlier acquisition may have been by the same local radar system or by a remote radar system in communication with the subject local radar system. The time of acquisition, the spatial coordinates and possibly a velocity vector (or similar pertinent elements of information) are reported from the remote radar system or otherwise known at the local radar system. Direction and speed may remain the same or may change due to active guidance or the influence of gravity. Changes are expected to be within practical limits. From reported information and a span of uncertainty, the covariance volume is inferred. With increasing time after an earlier acquisition, uncertainties in direction and speed multiply and the covariance ellipsoid enlarges. Using inferences from previous observation, probability factors and assumptions, the covariance ellipsoid is constructed logically. It is possible to mathematically define a covariance space in various ways, such as a sphere or cube or other shape. In the present examples, the covariance volume preferably is defined as an ellipsoid of predetermined size, shape, eccentricity and orientation in space.
In order to search the volume of the covariance ellipsoid, the outermost active beams in azimuth and elevation should encounter the extreme outer edges of the covariance ellipsoid. The inner beams should paint the entire projection of the covariance ellipsoid as viewed from the radar. Time devoted to beams in the pattern that do not intersect the covariance volume is wasted. Areas within the covariance volume that are not searched by an incident beam present a risk that the target located there may escape detection.
Mathematical methods have been proposed to project a covariance ellipses onto perpendicular planes that intersect the centers of azimuth and elevation of a radar system. The beams at the extremes of azimuth and elevation are tangents to the covariance ellipse in their respective plane and those beams can define the outer limits of the span of azimuth and elevation to be searched. The controller bypasses beams that are not oriented to intersect the projection of the covariance volume. What is needed is accurately to determine the outer extents of azimuth and elevation that correspond to the outer edges of the covariance volume from the viewpoint of the radar system, and preferably also to determine the maximum and minimum range of each beam.
U.S. patent application Ser. No. 12/879,374, entitled “Method for Scanning a Radar Search Volume and Correcting For 3D Orientation of Covariance Ellipsoid,” Mark Friesel, teaches use of a parallel projection. The full disclosure of said application is hereby incorporated by reference herein. The parallel projection technique is reasonably accurate but may cause the acquisition face to be offset from an ideal position, because a parallel projection employs a projection of the covariance ellipsoid at a nominal range, i.e., a projected outline of the ellipsoid on a surface parallel to the surface of the radar acquisition face. The outer limits of azimuth and elevation (the extents) are determined based on the edges of the projection at a nominal range of the covariance ellipsoid, projected onto azimuth and elevation planes intersecting the centers of the radar and of the covariance ellipsoid.
The radar acquisition face is effectively a shadow view, i.e., a silhouette in two dimensions, with a nominal azimuth center and elevation center, and azimuth and elevation extents on either side of center, and minimum and maximum ranges. A two dimensional projection of a covariance ellipsoid encompasses an ellipsoid of arbitrary orientation. However, parallel projection methods for determining search volumes produce less than ideal descriptors for the search volume. This occurs because the volume of the covariance ellipsoid as viewed from the radar system is affected by perspective. Elements of a shape that have a given size but are at a greater range from the observer have a smaller apparent size than elements of equal size at a nearer distance, which have a relatively larger apparent size. At the same time, the increasing area of the acquisition face with increasing range is such that any given beam encompasses a larger area at greater range than the same beam encompassed as shorter range.
What is needed is an efficient technique for defining descriptors for a search volume accurately, i.e., limits or extents of elevation, azimuth, and preferably range, and with a minimum of complication.